Finite Group Databasebeta

← C3×#70676 #11794324

Subgroups — C3×#70676 #11794324

Order 1152.

515 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#428C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4C3×#5001C211yesmaximal, characteristic
5C3×#4999C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic
7C3×#4530C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#70676C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#107—21no—
18C32×#106—21no—
19C3×#823—22no—
20C3×#822—22no—
21C3×#809—21no—
22C3×#809—21no—
23C3×#809—22no—
24C3×C4⋊(C3⋊C8)—22no—
25C2×C3×#108—31no—
26C3×#428—21no—
27C3×#428D311yescharacteristic, complemented
28C3×#428C2×C311yescharacteristic, complemented
29C3×#424—31no—
30C3×#418—31no—
31C2×C3×#102—31no—
32C2×C3×#100—31no—
33C2×#823C2×C311yescharacteristic
34C2×#822C2×C311yescharacteristic, complemented
35#5001C2×C311yescharacteristic
36#4999C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic
38C3×#343—31no—
39#4530C2×C311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C32×M16—21no—
50C32×M16D412yes—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C32×C42—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—31noSylow
68C22×C3×D4—31no—
69C22×D12C22×C311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C22×C3×C8—31no—
76C3×#117—21no—
77C3×#117C2×D311yescharacteristic
78C3×#117C22×C311yescharacteristic
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C22×C311yescharacteristic
82C2×#208C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—22no—
87C3×#107—21no—
88C3×#107—21no—
89C3×#106—22no—
90C3×#106—21no—
91C3×#106—21no—
92C3×C4⋊C8—62no—
93C3×#102—62no—
94C3×#102—61no—
95C3×#102—61no—
96C3×#100—62no—
97#823—22no—
98#822—22no—
99#809—21no—
100#809—21no—
101#809—22no—
102C4⋊(C3⋊C8)—22no—
103C23×C32#4111yescharacteristic
104C22×C3×D3—22no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—81no—
108C22×C3×D3—81no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—81no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C3×D12—22no—
120C3×D12—22no—
121C3×D12—41no—
122C3×D12—41no—
123C32×C8—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127C2×#108—31no—
128#428C3×D311yescharacteristic, complemented
129#424—31no—
130#418—31no—
131C2×#102—31no—
132C2×#100—31no—
133#343—31no—
134C24×C3—61no—
135C23×D3—21no—
136C2×C3×D4—32no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—41no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C23×C311yescharacteristic
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12C3×Q812yes—
154C3×M16—22no—
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—22no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16D1212yes—
163C3×M16C3×D412yes—
164C2×C3×C8—22no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—32no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4#6711yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C4⋊C4C3×D411yescharacteristic
183C3×C4⋊C4C3×D411yescharacteristic
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—41no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—41no—
190#208—21no—
191#208—21no—
192#208—21no—
193#208—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8C3×D412yes—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32#12111yescharacteristic
202C22×C32C22⋊Q811yescharacteristic
203C22×C32#12611yescharacteristic
204C2×C3×D3—42no—
205C2×C3×D3—82no—
206C2×C3×D3—81no—
207C2×C3×D3—81no—
208C2×C3×D3—82no—
209C32×C4—41no—
210C32×C4—41no—
211C32×C4—81no—
212C32×C4#12111yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C22×D4—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16C2×C3×D311yescharacteristic
220C22×C8—31no—
221#117C2×C3×D311yescharacteristic
222C2×C4⋊C4C2×C3×D311yescharacteristic
223#108—62no—
224#107—21no—
225#106—21no—
226C4⋊C8—62no—
227#102—62no—
228#102—61no—
229#102—61no—
230#100—62no—
231C23×C3—21no—
232C23×C3—62no—
233C23×C3—121no—
234C23×C3—121no—
235C23×C3—241no—
236C23×C3—241no—
237C23×C3#23711yescharacteristic
238C23×C3C3×#4111yescharacteristic
239C22×D3—22no—
240C22×D3—41no—
241C22×D3—41no—
242C22×D3—81no—
243C22×D3—81no—
244C3×D4—62no—
245C3×D4—62no—
246C3×D4—121no—
247C3×D4—121no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—82no—
264C2×C3×C4—81no—
265C2×C3×C4—81no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×Q811yescharacteristic
270C2×C3×C4#23911yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×Q811yescharacteristic
276C2×C3×C4C3×#4111yescharacteristic
277C2×C3×C4C3×#4111yescharacteristic
278D12—22no—
279D12—22no—
280D12—41no—
281D12—41no—
282C3×C8—24no—
283C3×C8—22no—
284C3×C8—22no—
285C3×C8—62no—
286C3×C8—121no—
287C3×C8—121no—
288C3⋊C8—22no—
289C3⋊C8—41no—
290C3⋊C8—41no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32#39611yescharacteristic
294C2×C32#47111yescharacteristic
295C2×C32#47211yescharacteristic
296C3×D3—82no—
297C24—61no—
298C2×D4—32no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C22×C4—21no—
305C22×C4C22×C3×D311yescharacteristic
306M16—21no—
307M16—61no—
308M16—61no—
309M16—61no—
310M16—61no—
311M16C3×D1212yes—
312C2×C8—21no—
313C2×C8—32no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—61no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4C3×#6711yescharacteristic
321C4⋊C4C3×#6711yescharacteristic
322C22⋊C4—21no—
323C42—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—122no—
334C22×C3—242no—
335C22×C3—242no—
336C22×C3—241no—
337C22×C3—241no—
338C22×C3#89711yescharacteristic
339C22×C3#89811yescharacteristic
340C22×C3#93911yescharacteristic
341C22×C3C3×#12111yescharacteristic
342C22×C3C3×C22⋊Q811yescharacteristic
343C22×C3C3×#12611yescharacteristic
344C2×D3—42no—
345C2×D3—82no—
346C2×D3—81no—
347C2×D3—81no—
348C2×D3—82no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—81no—
358C3×C4—81no—
359C3×C4—82no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4#89511yescharacteristic
363C3×C4#89611yescharacteristic
364C3×C4#93011yescharacteristic
365C3×C4#94611yescharacteristic
366C3×C4C3×#12111yescharacteristic
367C3×C4C3×#12111yescharacteristic
368C3×C4C3×C22⋊Q811yescharacteristic
369C3×C4C3×C22⋊Q811yescharacteristic
370C32#206311yescharacteristic, complemented, Sylow
371C23—62no—
372C23—121no—
373C23—121no—
374C23—241no—
375C23—241no—
376C23C3×#23711yescharacteristic
377D4—62no—
378D4—62no—
379D4—121no—
380D4—121no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×C3×D1211yescharacteristic
386C2×C4C3×#23511yescharacteristic
387C2×C4C3×D3×D411yescharacteristic
388C2×C4C3×D3×Q811yescharacteristic
389C2×C4C3×#23911yescharacteristic
390C2×C4C2×C3×#6711yescharacteristic
391C8—22no—
392C8—62no—
393C8—121no—
394C8—121no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—41no—
403C2×C3—41no—
404C2×C3—242no—
405C2×C3#499411yescharacteristic
406C2×C3#519911yescharacteristic
407C2×C3#520311yescharacteristic
408C2×C3C3×#39611yescharacteristic
409C2×C3C3×#47111yescharacteristic
410C2×C3C3×#47211yescharacteristic
411D3—82no—
412C22—21no—
413C22—21no—
414C22—122no—
415C22—242no—
416C22—242no—
417C22—241no—
418C22—241no—
419C22C3×#89711yescharacteristic
420C22C3×#89811yescharacteristic
421C22C3×#93911yescharacteristic
422C4—41no—
423C4—41no—
424C4—81no—
425C4C3×#89511yescharacteristic
426C4C3×#89611yescharacteristic
427C4C3×#93011yescharacteristic
428C4C3×#94611yescharacteristic
429C3—21no—
430C3#7067611yescharacteristic, direct product factor
431C3C3×#206311yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2—242no—
435C2C3×#499411yescharacteristic
436C2C3×#519911yescharacteristic
437C2C3×#520311yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#428C2
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC3×#428D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#428

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×#428C2semidirect
3. C2×C3×#822C2semidirect
5. C3×#4999C2semidirect
7. C3×#4530C2semidirect
9. #70676C3direct (N × H)
27. C3×#428D3semidirect
28. C3×#428C2×C3semidirect
34. C2×#822C2×C3semidirect
36. #4999C2×C3semidirect
39. #4530C2×C3semidirect
128. #428C3×D3semidirect
370. C32#2063semidirect
430. C3#70676direct (N × H)
431. C3C3×#2063semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#4282
C2×C3×#8232
C2×C3×#8222
C3×#50012
C3×#49992
C2×C3×#8092
C3×#45302
C3×#20633
#706763